A method of analysis is given for determining the temperature distribution in a semi-infinite, homogeneous solid initially at a constant temperature and then suddenly heated by convection so that a phase change occurs and the new phase is removed upon formation. The method appears applicable to problems involving melting, freezing, or sublimation and to situations where the environment temperature and heat-transfer coefficient vary with time. It consists of calculating the temperature before the phase change occurs, during the transient process of phase change, and after steady-state conditions are obtained if such is possible. During the transient process, a numerical or graphical method of solution may be used which is an extension of the Binder [1] method. Numerical results obtained with a digital computer are given for the case where the environment temperature and coefficient of heat transfer are constant and provide a method for determining the velocity and position of the moving phase front.